When all you have is a spectrum, everything looks like a point (on that line)
I get what you wish to say, but if one considers that line to encompass the totality of possible viewpoints then everybody falls on it somewhere. If you want to introduce a crazy axis at right angles to the ideology axis, then we can talk about quadrants rather than left and right and include more nuance
Some acts, although having political effect, aren't done as a result of holding a belief on the political spectrum (regardless of number of axes one uses to define that spectrum).
Sometimes acts are committed merely because the actor is evil, or not mentally sound. Such people can make statements that imply certain political beliefs, but even if such person adheres to those political beliefs, correlation does not prove causation.